In terms of equipment, tactics, unit types, the way they were raised, etc.
I wrote "English" because I assume many of the troops fighting for the King of England were French or Welsh, not just English. I suppose by "French" I really mean "fighting for the King of France" since I could be wrong in assuming they were all French. (Plus, I guess "French" was a much vaguer thing then)
An add-on question of sorts, how did the French army change after the battle of Agincourt? Did it adopt new anti-archer tactics?